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Previous issue date: 2014-02-25 / Conselho Nacional de Pesquisa e Desenvolvimento Científico e Tecnológico - CNPq / Inthiswork,basedonthearticlesMariaLuízaLeiteandOscasPalmas,wepresentedthe
classificationofthecompleterotationhypersurfaceswithconstantscalarcurvature,inRn
eHn withn>3. / Neste trabalho, baseado nos artigos de Maria Luíza Leite e Oscas Palmas, classificamos
as hipersuperfícies de rotação completas, com curvatura escalar constante, emRn eHn
comn>3.
| Identifer | oai:union.ndltd.org:IBICT/oai:repositorio.bc.ufg.br:tde/2967 |
| Date | 25 February 2014 |
| Creators | Carvalho, Marcos Túlio Alves de |
| Contributors | Pina, Romildo da Silva, Pina, Romildo da Silva, Araújo, Kellcio Oliviera, Pieterzack, Maurício Donizetti |
| Publisher | Universidade Federal de Goiás, Programa de Pós-graduação em Matemática (IME), UFG, Brasil, Instituto de Matemática e Estatística - IME (RG) |
| Source Sets | IBICT Brazilian ETDs |
| Language | Portuguese |
| Detected Language | English |
| Type | info:eu-repo/semantics/publishedVersion, info:eu-repo/semantics/masterThesis |
| Format | application/pdf |
| Source | reponame:Biblioteca Digital de Teses e Dissertações da UFG, instname:Universidade Federal de Goiás, instacron:UFG |
| Rights | http://creativecommons.org/licenses/by-nc-nd/4.0/, info:eu-repo/semantics/openAccess |
| Relation | 6600717948137941247, 600, 600, 600, 600, -4268777512335152015, 6357880884991220629, -2555911436985713659, [1] A.ROS. Compact hypersurfaces with constant scalar curvature and a congruence theorem. J. Diff. Geom. 27, 215-220 (1988). [2] COLARES, A. GERVASIO AND PALMAS, OSCAR. Addendum to: "Complete rotation hypersurfaces withHk constant in space forms"by Palmas. Bull. Braz. Math. Soc. (N.S.) 39, n◦ 1, 11-20, (2008). [3] DELAUNAY, C. Sur la surface de révolution don‘t la courbure moyenne est constant. J. Math. pure et appl, Série 16, (1841). [4] DO CARMO, M. P. AND DAJCZER, M. Rotation hypersurfaces in spaces of constant curvature. Transactions of the American Mathematical Society 277-2, p.685-709, (1993). [5] DO CARMO, M. P. Geometria Diferencial de curvas e Superfícies. Rio de Janeiro, SBM, (2010). [6] DO CARMO, M. P. Geometria Riemanniana. Projeto Euclides, Rio de Janeiro. quinta edição, (2011). [7] FILHO, R. S. V. A. AND CHAVES, R. M. B. Noçõesfundamentaissobregráficos no espaço hiperbólicoH3. USP. [8] GUIMARÃES, TULIO AND SATO, JOCELINO Hipersuperfícies doR4 com curvatura escalar nula invariantes por um subgrupo de isometrias. Anais do I Congresso de Matemática Aplicada e Computacional da Região Sudeste, (2011). [9] HSIANG, W. Y AND LAWSON, H. B. Minimal submanifolds of low cohomegeneity, Journal of Differential Geometry. vol. 5, p.1-38, (1971). [10] HSIANG, W. Y. OnrotationalW-hypersurfacesinspacesofconstantcurvature and generalized laws of sine and cosine. Bull. Inst. Math. Acad. Sinica 11, 349373, (1977). [11] HSIANG, W. Y. On W- hypersurfaces of generalized rotational type inEn+1, I, preprint, (1982). [12] J. L. BARBOSA AND M. DO CARMO: Helicoids, catenoids and minimal hypersurfaces ofRn invariant by an l - parameter group of motions. An. Acad. Bras. Cienc. 53, 403-408, (1981). [13] LEITE, M. L. Rotation hypersurfaces of space forms with constant scalar curvature. Manuscripta. 67, 285 - 304, (1990). [14] LI, HAIZHONG AND WEI, GUOXIN. Embedded rotational hypersurfaces with constant scalar curvature inSn. A correction to a statement:"Rotational hypersurfaces of space forms with constant scalar curvature" by M. L. LEITE. Manuscripta Math. 120, n◦ 3, 319-323, (2006). [15] LI, HAIZHONG AND WEI, GUOXIN. Compactembeddedrotationhypersurfaces ofSn. Bull. Braz. Math. Soc. (N.S.) 38, n◦ 1, 81-99, (2007). 17] PALMAS, OSCAR. CompleterotationhypersurfaceswithHk constantinspace forms. Bol. Soc. Brasil. Mat. (N.S.) 30, n◦ 2, 139-161, (1999). [18] PINA, ROMILDO. Hipersuperfíciesderotaçãocomcurvaturaescalarconstante negativa. Dissertação de Mestrado, UNB - Brasília, (1992). [19] S. Y. CHENG AND S. T. YAU: Hypersurfaces with constant scalar curvature, Math. Ann. 225, 195-204. (1977). [20] SPIVAK, M. A comprehensive introduction to Differential Geometry, vol 4, 2nd edn, Publish or Perish, Inc. Berkeley, (1979). |
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